The origin of upper bound on \(\lambda \)  above can be seen from the beta function \(\beta _{\lambda }\)  for \(\lambda \) .
Since \(\beta _{\lambda }\)  is dominated by the top Yukawa coupling \(y_t\) ,
the sign of which is positive,
it imposes an upper bound on the EW value of \(\lambda \) 
in order to be still in the perturbative region at high energy scale.
Given this scale near the grand unification (GUT) scale \(\simeq 1.0\times 10^{15}\)  GeV,
the critical value was found to be \(\sim 0.7\)  [1]} in terms of the one-loop beta function
In this paper, we follow the convention in [2]},
and present our \(\beta \)  functions in the \(\overline{DR}\)  scheme.,
\({}\beta _{\lambda }=\frac{\lambda }{16\pi ^{2}}\left[4\lambda ^{2}+3y^{2}_{t}+2\kappa ^{2}-3g^{2}_{2}-\frac{3}{5}g^{2}_{1}\right],\) 
